import System( getArgs ) import Text.Printf import Data.List import Data.Maybe import Data.Set( Set ) import qualified Data.Set as Set import Data.Map( Map, (!) ) import qualified Data.Map as Map import TypeVar import Term import Theorem import Object import Parse import Stack( Stack, at, (<:>) ) import qualified Stack as Stack import qualified Command as Com type MachineState = Maybe (Stack Object, Map Int Object, --dictionary Set Theorem, --assumptions Set Theorem) --theorems machineToString :: MachineState -> Maybe String machineToString x = do (s,d,a,t) <- x let s' = show s d' = "Dictionary:\n" ++ intercalate "\n" (map (show) (Map.toList d)) ++ "\n\n" a' = "Assumptions:\n" ++ intercalate "\n" (map (show) (Set.toList a)) ++ "\n\n" t' = "Theorems:\n" ++ intercalate "\n" (map (show) (Set.toList t)) ++ "\n\n" return (s' ++ d' ++ a' ++ t') data ArticleLine = Comment { commentString :: String } | Command { commandFunc :: (MachineState -> MachineState) } parse :: String -> ArticleLine parse "absTerm" = Command absTerm parse "absThm" = Command absThm parse "appTerm" = Command appTerm parse "appThm" = Command appThm parse "assume" = Command assume parse "axiom" = Command axiom parse "betaConv" = Command betaConv parse "cons" = Command cons parse "const" = Command constant parse "constTerm" = Command constTerm parse "deductAntisym" = Command deductAntisym parse "def" = Command def parse "defineConst" = Command defineConst parse "defineTypeOp" = Command defineTypeOp parse "eqMp" = Command eqMp parse "nil" = Command nil parse "opType" = Command opType parse "pop" = Command pop parse "ref" = Command ref parse "refl" = Command refl parse "remove" = Command remove parse "subst" = Command subst parse "thm" = Command thm parse "typeOp" = Command typeOp parse "var" = Command var parse "varTerm" = Command varTerm parse "varType" = Command varType parse s@('#':rest) = Comment s parse s@('"':rest) = Command (name s) parse n = Command (number n) name :: String -> (MachineState -> MachineState) name str = \x -> do (s,d,a,t) <- x n <- Com.name str let s' = (ObjName n) <:> s return (s',d,a,t) number :: String -> (MachineState -> MachineState) number n = \x -> do (s,d,a,t) <- x num <- Com.number n let s' = (ObjNum num) <:> s return (s',d,a,t) absTerm :: MachineState -> MachineState absTerm x = do (s,d,a,t) <- x te <- (s `at` 0) >>= objTerm; v <- (s `at` 1) >>= objVar let term = Com.absTerm te v s' = (ObjTerm term) <:> (Stack.pop 2 s) return (s',d,a,t) absThm :: MachineState -> MachineState absThm x = do (s,d,a,t) <- x th <- (s `at` 0) >>= objThm; v <- (s `at` 1) >>= objVar thm <- Com.absThm th v let s' = (ObjThm thm) <:> (Stack.pop 2 s) return (s',d,a,t) appTerm :: MachineState -> MachineState appTerm x = do (s,d,a,t) <- x f <- (s `at` 0) >>= objTerm; x <- (s `at` 1) >>= objTerm let term = Com.appTerm f x s' = (ObjTerm term) <:> (Stack.pop 2 s) return (s',d,a,t) appThm :: MachineState -> MachineState appThm x = do (s,d,a,t) <- x t1 <- (s `at` 0) >>= objThm; t2 <- (s `at` 1) >>= objThm let thm = Com.appThm t1 t2 s' = (ObjThm thm) <:> (Stack.pop 2 s) return (s',d,a,t) assume :: MachineState -> MachineState assume x = do (s,d,a,t) <- x te <- (s `at` 0) >>= objTerm thm <- Com.assume te let s' = (ObjThm thm) <:> (Stack.pop 1 s) return (s',d,a,t) axiom :: MachineState -> MachineState axiom x = do (s,d,a,t) <- x te <- (s `at` 0) >>= objTerm; l <- (s `at` 1) >>= objList thm <- Com.axiom te (mapMaybe objTerm l) let s' = (ObjThm thm) <:> (Stack.pop 2 s) a' = Set.insert thm a return (s',d,a',t) betaConv :: MachineState -> MachineState betaConv x = do (s,d,a,t) <- x te <- (s `at` 0) >>= objTerm let thm = Com.betaConv te s' = (ObjThm thm) <:> (Stack.pop 1 s) return (s',d,a,t) cons :: MachineState -> MachineState cons x = do (s,d,a,t) <- x l <- (s `at` 0) >>= objList; h <- (s `at` 1) let s' = (ObjList $ h : l) <:> (Stack.pop 2 s) return (s',d,a,t) constant :: MachineState -> MachineState constant x = do (s,d,a,t) <- x n <- (s `at` 0) >>= objName let constant = Com.constant n s' = (ObjConst constant) <:> (Stack.pop 1 s) return (s',d,a,t) constTerm :: MachineState -> MachineState constTerm x = do (s,d,a,t) <- x ty <- (s `at` 0) >>= objType; c <- (s `at` 1) >>= objConst let term = Com.constTerm ty c s' = (ObjTerm term) <:> (Stack.pop 2 s) return (s',d,a,t) deductAntisym :: MachineState -> MachineState deductAntisym x = do (s,d,a,t) <- x t1 <- (s `at` 0) >>= objThm; t2 <- (s `at` 1) >>= objThm let thm = Com.deductAntisym t1 t2 s' = (ObjThm thm) <:> (Stack.pop 2 s) return (s',d,a,t) def :: MachineState -> MachineState def x = do (s,d,a,t) <- x num <- (s `at` 0) >>= objNum; obj <- (s `at` 1) let d' = Map.insert num obj d s' = Stack.pop 1 s return (s',d',a,t) defineConst :: MachineState -> MachineState defineConst x = do (s,d,a,t) <- x te <- (s `at` 0) >>= objTerm; n <- (s `at` 1) >>= objName (thm, constant) <- Com.defineConst te n let s' = (ObjThm thm) <:> (ObjConst constant) <:> (Stack.pop 2 s) return (s',d,a,t) defineTypeOp :: MachineState -> MachineState defineTypeOp x = do (s,d,a,t) <- x th <- (s `at` 0) >>= objThm; l <- (s `at` 1) >>= objList; r <- (s `at` 2) >>= objName ab <- (s `at` 3) >>= objName; y <- (s `at` 4) >>= objName (rthm, athm, rep, abst, n) <- Com.defineTypeOp th (mapMaybe objName l) r ab y let s' = (ObjThm rthm) <:> (ObjThm athm) <:> (ObjConst rep) <:> (ObjConst abst) <:> (ObjTyOp n) <:> (Stack.pop 5 s) return (s',d,a,t) eqMp :: MachineState -> MachineState eqMp x = do (s,d,a,t) <- x t1 <- (s `at` 0) >>= objThm; t2 <- (s `at` 1) >>= objThm thm <- Com.eqMp t1 t2 let s' = (ObjThm thm) <:> (Stack.pop 2 s) return (s',d,a,t) nil :: MachineState -> MachineState nil x = do (s,d,a,t) <- x return (ObjList [] <:> s, d, a, t) opType :: MachineState -> MachineState opType x = do (s,d,a,t) <- x l <- (s `at` 0) >>= objList; to <- (s `at` 1) >>= objTyOp let newType = Com.opType (mapMaybe objType l) to s' = (ObjType newType) <:> (Stack.pop 2 s) return (s',d,a,t) pop :: MachineState -> MachineState pop x = do (s,d,a,t) <- x return ((Stack.pop 1 s),d,a,t) ref :: MachineState -> MachineState ref x = do (s,d,a,t) <- x n <- (s `at` 0) >>= objNum let object = d ! n s' = object <:> (Stack.pop 1 s) return (s',d,a,t) refl :: MachineState -> MachineState refl x = do (s,d,a,t) <- x te <- (s `at` 0) >>= objTerm let thm = Com.refl te s' = (ObjThm thm) <:> (Stack.pop 1 s) return (s',d,a,t) remove :: MachineState -> MachineState remove x = do (s,d,a,t) <- x n <- (s `at` 0) >>= objNum let object = d ! n s' = object <:> (Stack.pop 1 s) d' = Map.delete n d return (s',d',a,t) subst :: MachineState -> MachineState subst x = do (s,d,a,t) <- x th <- (s `at` 0) >>= objThm; l <- (s `at` 1) >>= objList thm <- Com.subst th l let s' = (ObjThm thm) <:> (Stack.pop 2 s) return (s',d,a,t) thm :: MachineState -> MachineState thm x = do (s,d,a,t) <- x te <- (s `at` 0) >>= objTerm; l <- (s `at` 1) >>= objList; th <- (s `at` 2) >>= objThm thm <- Com.thm te (mapMaybe objTerm l) th let s' = Stack.pop 3 s t' = Set.insert thm t return (s',d,a,t') typeOp :: MachineState -> MachineState typeOp x = do (s,d,a,t) <- x n <- (s `at` 0) >>= objName let typeOp = Com.typeOp n s' = (ObjTyOp typeOp) <:> (Stack.pop 1 s) return (s',d,a,t) var :: MachineState -> MachineState var x = do (s,d,a,t) <- x ty <- (s `at` 0) >>= objType; n <- (s `at` 1) >>= objName v <- Com.var ty n let s' = (ObjVar v) <:> (Stack.pop 2 s) return (s',d,a,t) varTerm :: MachineState -> MachineState varTerm x = do (s,d,a,t) <- x v <- (s `at` 0) >>= objVar let term = Com.varTerm v s' = (ObjTerm term) <:> (Stack.pop 1 s) return (s',d,a,t) varType :: MachineState -> MachineState varType x = do (s,d,a,t) <- x n <- (s `at` 0) >>= objName newType <- Com.varType n let s' = (ObjType newType) <:> (Stack.pop 1 s) return (s',d,a,t) doSemanticCheck :: [String] -> String doSemanticCheck list = let s = Stack.empty d = Map.empty a = Set.empty t = Set.empty op = (\x y -> case y of (Comment _) -> x (Command z) -> z x) -- important to use foldl here so commands get applied in the correct order result = (foldl' (op) (Just (s,d,a,t))) . (map (parse)) $ list in case (machineToString result) of Just x -> x Nothing -> "Error\n" main = do args <- getArgs list <- getLines $ head args let result = doSemanticCheck (map (stripReturn) list) printf result